Optimal Synthesis of a Satellite Attitude Control System under Constraints on Control Torques and Speeds of Reaction Wheels

The goal is the optimal synthesis of the parameters of the control law for a nonlinear satellite attitude control system under constraints related to the saturation effect of reaction wheels. The maximum stability degree of the control system is considered as a criterion for the optimality of the parameters of the control law, and the absolute values of the control torques and angular velocities of the reaction wheels, achievable within the limits of the physical characteristics of the drives, are considered as constraints. The solution to the optimal synthesis problem is based on the transformation of the nonlinear control system model into a linear model, within the framework of the problem of global asymptotic stability of the control system is also guaranteed. The problem is decomposed into a subproblems of obtaining the optimal transient process shape in the control system and considering the constraints. A method of synthesizing the optimal transient process shape based on the criterion of maximum stability degree had been developed. An analytical method of determining the optimal values of the control law parameters, based on decomposing the normalized characteristic polynomial in the linear model into three identical factors had been proposed. A method with regards to the constraints of the control torque and angular speed of the reaction wheels, based on transitioning from relative to real time is developed. An algorithm for calculation of the transition scale from relative to real time, ensuring the fulfillment of all constraints in the optimal synthesis problem, is proposed. An example demonstrating the efficiency and simplicity of the proposed methods and algorithm for targeted selection of technical characteristics of the control system, considering the maximum absolute values of angular speeds and control torques of the reaction wheels, is provided.